Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 897 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.What is the 20th term of the AP 14, 19, 24, 29, …? (a) 100 (b) 114 (c) 95 (d) 109
2. 2.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 6 (b) 9 (c) 10 (d) 7
4. 4.What is the mean of 6, 10, 9, 19, 14 and 20? (a) 15 (b) 13 (c) 14 (d) 12
5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
6. 6.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 120 (d) 128
7. 7.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/6 (c) 1/3 (d) 5/6
8. 8.What is the median of 23, 29, 24, 10 and 22? (a) 23 (b) 24 (c) 25 (d) 22
9. 9.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 200 (d) 193
10. 10.What is the mode of 12, 4, 4, 8, 8, 2 and 4? (a) 8 (b) 2 (c) 4 (d) 12
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
12. 12.Which term of the AP 15, 21, 27, 33, … is 81? (a) 13th (b) 12th (c) 14th (d) 11th
13. 13.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 120° (b) 160° (c) 60° (d) 140°
14. 14.In a class of 41 children, 25 like cricket, 13 like football and 7 like both. How many like at least one of the two? (a) 41 (b) 38 (c) 31 (d) 24
15. 15.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 324 cu cm (d) 486 cu cm
16. 16.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
17. 17.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 30 (c) 10 (d) 24
18. 18.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
19. 19.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 232 (c) 240 (d) 231
20. 20.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 20 (d) 25
21. 21.What is the distance between the points (4, 1) and (16, 10)? (a) 16 (b) 21 (c) 225 (d) 15
22. 22.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
23. 23.In a class of 43 children, 27 like mangoes, 23 like bananas and 10 like both. How many like neither? (a) 13 (b) 10 (c) 3 (d) 4
24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
25. 25.What is the midpoint of the line joining (2, 10) and (4, 14)? (a) (6, 24) (b) (12, 3) (c) (3, 12) (d) (1, 2)
26. 26.A bag has 6 red, 5 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 8/13 (c) 9/13 (d) 5/13
27. 27.A cuboid is 9 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 18 cu cm (b) 108 cu cm (c) 168 cu cm (d) 17 cu cm
28. 28.What is the 33rd term of the AP 3, 9, 15, 21, …? (a) 192 (b) 195 (c) 198 (d) 201
29. 29.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
30. 30.What is the median of 38, 22, 8, 18, 2, 17 and 6? (a) 18 (b) 8 (c) 16 (d) 17
31. 31.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 10° (d) 280°
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 25 (d) 10
34. 34.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 9801 (b) 10201 (c) 10001 (d) 10211
35. 35.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 8 (c) 27 (d) 72
36. 36.A bag has 3 white, 4 green and 2 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 4/9 (b) 5/9 (c) 2/3 (d) 1/3
37. 37.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 1/4 (d) 5/6
38. 38.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7 (d) 5 × 7²
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
40. 40.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 60 (d) 55

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